time-dependent noise strength for FRs, particularly the IFR. To this
end, we recall
[1]}, [2]}, [3]} that
the key ingredient for the derivation of FRs from the LE is the
probability of observing a certain path of the particle. For an
arbitrary Gaussian process \(\xi (t)\) , such as the one in
Eq. (REF ), the conditional path probability that the
particle is at position \(x(t)\)  at time \(t\) , given that it was at
\(x(0)\)  at \(t=0\) , is given by [4]}, [5]}
\(P[x(t)|x(0)]= \exp \left[ - \frac{1}{2}\int _0^t dt_2\int _0^t dt_1 {\xi }(t_1)G(t_1,t_2) {\xi }(t_2)\right],\) 
